On an application of the Boundary control method to classical moment problems.

We establish relationships between the classical moments problems which are problems of a construction of a measure supported on a real line, on a half-line or on an interval from prescribed set of moments with the Boundary control approach to a dynamic inverse problem for a dynamical system with discrete time associated with Jacobi matrices. We show that the solution of corresponding truncated moment problems is equivalent to solving some generalized spectral problems.

Linear Positional and Speed Control of Servo Carts Using Inverse Dynamic Control

Dynamic inverse- (DI-) based control technique has been utilized in many applications and proven to be effective. Recently, the inverse dynamic control (IDC), an expansion to the classical DI technique, has been trending with implementation in many areas. It has been proved that IDC is capable of overcoming some limitations in DI-based techniques, particularly in cancellation of useful nonlinearities. This paper extends the implementation of IDC on the positional and speed control of the linear servo cart system. Simulation results further proves that IDC is an effective and robust controller evidently when comparing it with the proportional velocity and lead compensator controller.

Cooperative Guidance Law against Highly Maneuvering Target with Dynamic Surrounding Attack

In this paper, a new dynamic surrounding attack cooperative guidance law against highly maneuvering target based on decoupled model is proposed. First, a new dynamic surrounding guidance strategy is proposed, and virtual targets are introduced to establish the cooperative guidance model for dynamic surrounding attack. Second, a dynamic inverse method is used to decouple the cooperative guidance model, and extended state observers (ESOs) are introduced to estimate the disturbances caused by target maneuver. Then, the impact time and dynamic surrounding guidance (ITDSG) law against highly maneuvering target is designed based on a prescribed-time stable method and the decoupled model. Finally, numerical simulations are performed to illustrate the superiority and effectiveness of the proposed ITDSG.

Inverse problems for finite Jacobi matrices and Krein–Stieltjes strings

We consider dynamic inverse problems for a dynamical system associated with a finite Jacobi matrix and for a system describing propagation of waves in a finite Krein–Stieltjes string. We offer three methods of recovering unknown parameters: entries of a Jacobi matrix in the first problem and point masses and distances between them in the second, from dynamic Dirichlet-to-Neumann operators. We also answer a question on a characterization of dynamic inverse data for these two problems.

Deformation Reconstruction and High-Precision Attitude Control of a Launch Vehicle Based on Strain Measurements

The development of launch vehicles has led to higher slenderness ratios and higher structural efficiencies, and the traditional control methods have difficulty in meeting high-quality control requirements. In this paper, an incremental dynamic inversion control method based on deformation reconstruction is proposed to achieve high-precision attitude control of slender launch vehicles. First, the deformation parameters of a flexible rocket are obtained via fiber Bragg grating (FBG) sensors. The deformation and attitude information is introduced into the incremental dynamic inverse control loop, and an attitude control framework that can alleviate bending vibration and deformation is established. The simulation results showed that the proposed method could accurately reconstruct the shapes of flexible launch vehicles with severe vibration and deformation, which could improve the accuracy and stability of attitude control.

Design and Validation of Disturbance Rejection Dynamic Inverse Control for a Tailless Aircraft in Wind Tunnel

This paper focuses on the design of a disturbance rejection controller for a tailless aircraft based on the technique of nonlinear dynamic inversion (NDI). The tailless aircraft model mounted on a three degree-of-freedom (3-DOF) dynamic rig in the wind tunnel is modeled as a nonlinear affine system subject to mismatched disturbances. First of all, a baseline NDI attitude controller is designed for sufficient stability and good reference tracking performance of the nominal system. Then, a nonlinear disturbance observer (NDO) is supplemented to the baseline NDI controller to estimate the lumped disturbances for compensation, including unmodeled dynamics, parameter uncertainties, and external disturbances. Mathematical analysis demonstrates the convergence of the employed NDO and the resulting closed-loop system. Furthermore, an anti-windup modification is applied to the NDO for control performance preserving in the presence of actuator saturation. Subsequently, the designed control schemes are preliminarily validated and compared via simulations. The baseline NDI controller demonstrates satisfactory attitude tracking performance in the case of nominal simulation; the NDO augmented NDI controller presents significantly improved ability of disturbance rejection when compared with the baseline NDI controller in the case of robust simulation; the anti-windup modified scheme, rather than the baseline NDI controller nor the NDO augmented NDI controller, can preserve the closed-loop performance in the case of actuator saturation. Finally, the baseline NDI scheme and the NDO augmented NDI scheme are implemented and further validated in the wind tunnel flight tests, which demonstrate that the experimental results are in good agreement with that of the simulations.

Dynamic inverse piezo-effect problem for a long piezoceramic thermoelastic cylinder

Objective. The objective of this work is to solve an unrelated dynamic problem of thermoelectroelasticity for a long hollow piezoceramic cylinder under the action of an electric load on its surfaces in the form of a potential difference.Methods. The mathematical formulation of the considered problem of thermoelectroelasticity includes a system of non-selfadjoint differential equations. At the first stage, the authors consider the associated inverse piezoelectric effect problem without taking into account the influence of the temperature field, and at the next stage, study the hyperbolic heat conduction problem (Lord–Shulman theory) for a given (defined) electroelastic field.Result. A new closed solution to the dynamic inverse piezoelectric effect problem for a long piezoceramic thermoelastic cylinder is constructed. The case of the action of a dynamic electric load in the form of a potential difference on its front surfaces is considered. The ambient temperature and the law of convection heat transfer (3-kind boundary condition) are set. The calculated relations obtained using the generalized method of finite integral transformations allow determining the stress-strain state and thermoelectric fields induced in a piezoceramic element under an arbitrary electrical external influence.Conclusion. The constructed solution allows determining the stress-strain state and electric field in a piezoceramic cylinder, as well as analyzing the effect of the induced temperature field on the electroelastic state of the system under consideration using the hyperbolic Lord–Shulman theory of thermal conductivity. Analysis of the numerical results allows concluding that there are insignificant energy losses associated with heating the electroelastic system. The developed calculation algorithm is used in the design of non-resonant and resonant piezoelectric measuring devices.